A FAS approach for stabilization of generalized chained forms: part 1. Discontinuous control laws

In this paper, a type of general nonholonomic systems is proposed, which contains both the Brockett's two example systems, and their extended n-dimensional chained forms, as special cases. For the stabilization of such systems, a stabilizing controller is proposed based on the fully actuated system (FAS) approach, which is discontinuous at the origin but time-invariant when the open-loop system is time-invariant, and drives the feasible trajectories of the system to the origin exponentially. Furthermore, the proposed FAS approach is also extended to the sub-normal system case and the time-delay system case.